A numerical control device has been proposed for turning. The numerical control device includes a cutting-tool feed mechanism that feeds a cutting tool with respect to a workpiece and a control mechanism that controls the cutting-tool feed drive motor such that the cutting tool vibrates at a low frequency (see, for example, Patent Literatures 1 to 3). In this numerical control device, the control mechanism includes an operation unit that performs various settings, a vibration-cutting-information storage unit that has stored therein in advance at least the amount of forward movement, the amount of backward movement, the speed of forward movement, and the speed of backward movement of the cutting-tool feed mechanism according to mechanical characteristics such as the inertia of the feed axis or motor characteristics, as a table of data to synchronize and feed the cutting tool so as to be operable at a low frequency of 25 hertz or higher according to the rotational speed of the workpiece or the amount of feed of the cutting tool per revolution of the cutting tool, which is set by the operation unit, and a motor control unit that controls the cutting-tool feed drive motor on the basis of the data stored in the vibration-cutting-information storage unit. With this configuration, forward movement and backward movement are repeated along an interpolation path, thereby generating low-frequency vibrations.